Objectives:
Students will learn about the Transit of Venus through reading a NASA press release and viewing a NASA eClips video that describes several ways to observe transits. Then students will study angular measurement by learning about parallax and how astronomers use this geometric effect to determine the distance to Venus during a Transit of Venus.

Mathematics Skill or Topic Area:

Applications of Angular Measure

Next
Gen Science Standards:
PS3: Energy; ETS 1: Engineering Design

Common
Core ELA for Science:
RST.6-8.2. Determine the central ideas or conclusions of a text; provide an accurate summary of the text distinct from prior
knowledge or opinions; RST.6-8.8. Distinguish among facts, reasoned judgment based on research findings, and speculation in a text. RST.6-8.9. Compare and contrast the information gained from experiments, simulations, video,
or multimedia sources with that gained from reading a text on the same topic.

Common
Core Math Standard:CC.7.G.2 Draw geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides.

Video
Engagement: Transits
Discover how scientists used the last Venus transit and a geometric technique called
parallax to verify the distance between the sun and Earth. Find out what scientists hope to learn the next
time Venus transits the face of the sun in June 2012 (5 minutes).
View
Program

Engage
your students with a press release:

Venus Transit: A Celestial Rarity

NASA joined the world in viewing a rare celestial event, one not seen by any person now alive. The planet Venus appeared to cross in front of the Sun as seen from Earth. The last "Venus transit" occurred more than a century ago, in 1882, and was used to compute the distance from the Earth to the Sun. Scientists with NASA's Kepler mission hope to discover Earth-like planets outside our solar system by searching for transits of other stars by planets that might be orbiting them.

The Venus transit was visible over about 75 percent of the Earth, and ended at sunrise over central and eastern North America. The event was over by the time the Sun rises over the West Coast of North America (but viewers in Alaska could see the beginning of the transit and, for Northern Alaskans, the entire transit, because the Sun does not go below the horizon).

If people missed the June 8 Venus transit, they will have another chance in 2012 (June 6). After that, there will not be another Venus transit until 2117 (December 11).

During the 19th century, Venus transits were essential for astronomers to fathom the scale of the heavens, because they were used to give a relatively accurate distance from the Earth to the Sun. So critical was this measurement that, beginning in 1761, leading nations sent expeditions to remote corners of the globe to time exactly when Venus appeared to begin its transit of the Sun. The precise timing of the transit depended on location because different places on the globe saw the event from different angles. The times were compared and the distance to the Sun calculated using the known distances between expedition locations on the Earth and trigonometry.

The transit phenomenon has relevance to the future of astronomy as well. There is evidence for more than 100 extrasolar planets (planets outside our solar system) around other nearby stars. However, current techniques can only detect large planets, gas giants like Jupiter. But a star might have a planet that appears to pass in front of it by chance alignment with the Earth, and planets similar in size to the Earth could be detected if they transit their parent star.

Problem I - Angular Size and Similar Triangles -
-
A critical concept in astronomy is angular size, measured in degrees, minutes or arc-seconds. This is a review of
the basic properties of similar triangles for a fixed angle. Topics include geometry, similar triangles and proportions.
[Open
PDF]

Problem II - The Last Total Solar Eclipse--Ever!
-
Students explore the geometry required for a total solar eclipse, and estimate how many years into the future the last total
solar eclipse will occur as the moon slowly
recedes from Earth by 3 centimeters/year. Topics include angular measure and rates of change.
[Open PDF]

Explain
your thinking:

Write
your own problem- Using information
found in the Math Connection problems, the press release or the video
program, create your own math problem that involves angle measure or parallax. Explain why you set the problem up this
way, and how you might find its answer.

Evaluate
your understanding:

Challenge Problem
- Imagine looking down on a scale model of the solar system showing the concentric
circular orbits of Venus and Earth with our sun at the center.
On March 26, 2012 the angle between the Earth, Sun and Venus (ESV) measured 45 degrees. The angle between Venus, Earth and the Sun (VES)
measured 46 degrees and the angle between Earth, Venus and the Sun (EVS) measured 89 degrees. As viewed in the evening sky from Earth,
what will be the angular separation between Venus and the Sun at sunset? You might want to draw a scaled model to help you visualze the angles. Explain how you arrived at your answer.

Answer: The relevant angle is VES which is 46 degrees. Astronomers call this the Greatest Eastern Elongation of Venus.

NASA
/ JPL

3-D
Solar System

Extend
your new knowledge - Students use the Eyes on the Solar System simulator to study the geometry of the transit of Venus, and use what they have learned to predict the transit for the year 2125.
[ Open
PDF ]